Freethought & Rationalism Archive

Answerer · 09-28-2002, 07:50 PM

Hi guys, I realize that no one here like to discuss magnetism, nevertheless, I have some questions that need some answers. Please help me out:

1)Is magnetism a relativistic phenomenon of electric force and if so, why?

2)Or is magnetism a force created by magnetic monopole(if there is such a thing)?

Jesse · 09-28-2002, 08:24 PM

#1. Since magnetism only appears when you have moving charges, it has to do with Lorentz contraction due to charges moving relative to one another--here's a page summarizing how it works:

<a href="http://physics.weber.edu/schroeder/mrr/MRRtalk.html" target="_blank">http://physics.weber.edu/schroeder/mrr/MRRtalk.html</a>

Answerer · 09-29-2002, 02:56 AM

Thanks again, anyway, if magnetic monopoles are found to be in actual existence, don't this destory the stand that magnetism is merely a relativistic effect of the eletric force?

Feather · 09-29-2002, 03:26 AM

Now that's an interesting take on things. Hell, I've never been exposed to this treatment. Of course, I just started grad school last month.

Of course, if a magnetic monopole were discovered, that'd toss this particular treatment right out the window as a mere mathematical oddity.

Or it could have implications for quantum mechanics (why should the existence of a given class of particle interact just so?).

Fortunately electromagnetic theory as it is usually taught now would not change overmuch, since the introduction of a magnetic monopole preserves the symmetry in Maxwell's Equations.

Jesse · 09-29-2002, 03:51 AM

Answerer:
Thanks again, anyway, if magnetic monopoles are found to be in actual existence, don't this destory the stand that magnetism is merely a relativistic effect of the eletric force?

It wouldn't change the fact that for matter that does not contain magnetic monopoles, the magnetic field can be derived as a consequence of the coulomb force and relativity. Even the theories that postulate magnetic monopoles do not say that they are the cause of magnetism in normal matter--they are expected to be pretty rare, I believe. The existence of magnetic monopoles might just demonstrate that the relation between coulomb and magnetic forces is completely symmetrical, since uncharged magnetic monopoles would presumably generate a coulomb force when you move them around, as a consequence of relativity again.

[ September 29, 2002: Message edited by: Jesse ]

Answerer · 09-29-2002, 05:59 AM

Well, are you suggesting that if magnetic monopoles are to be discovered, they can't be static or stationary and are sure to move about and generating electric force at the same time?
Anyway, how are magnetic charges(if there is) and electric charges related to planck constant?

[ September 29, 2002: Message edited by: Answerer ]

Feather · 09-29-2002, 06:26 AM

Quote:

Originally posted by Answerer:
Well, are you suggesting that if magnetic monopoles are to be discovered, they can't be static or stationary and are sure to move about and generating electric force at the same time?
Anyway, how are magnetic charges(if there is) and electric charges related to planck constant?

[ September 29, 2002: Message edited by: Answerer ]

Charge isn't necessarily related to planck's constant in any fundamental way.

As for the other, no charge is ever actually at rest except within its own inertial frame. This applies to electric charges now, and would likely apply to magnetic monopoles as well.

Jesse · 09-29-2002, 06:31 AM

Answerer:
Well, are you suggesting that if magnetic monopoles are to be discovered, they can't be static or stationary and are sure to move about and generating electric force at the same time?

I'm not sure what you mean. I'm suggesting that they'd be much like charged particles, in the sense that if two are stationary with respect to each other there'd be no coulomb force between them (just like there's no magnetic force between stationary charged particles), but if they were moving with respect to each other there'd be a coulomb force as well as a magnetic force.

Answerer:
Anyway, how are magnetic charges(if there is) and electric charges related to planck constant?

Not sure about this--it might involve QED (quantum electrodynamics) which I haven't studied. According to <a href="http://superstringtheory.com/history/history3.html" target="_blank">this</a> page, in 1931 "Dirac shows that the existence of magnetic monopoles would lead to electric charge quantization." Actually that page is on superstring theory, and I remember from somewhere that superstring theory is supposed to explain the "duality" between the magnetic force and the coulomb force--ie the perfect symmetry between the two forces in the Maxwell equations. So understanding these issues fully may require some pretty advanced physics. Here's an article on M-theory (which encompasses superstring theory) that talks about duality a bit:

<a href="http://www.mkaku.org/mtheory.html" target="_blank">http://www.mkaku.org/mtheory.html</a>

Quote:

Loosely speaking, two theories are "dual" to each other if they can be shown to be equivalent under a certain interchange. The simplest example of duality is reversing the role of electricity and magnetism in the equations discovered by James Clerk Maxwell of Cambridge University 130 years ago. These are the equations which govern light, TV, X-rays, radar, dynamos, motors, transformers, even the Internet and computers. The remarkable feature about these equations is that they remain the same if we interchange the magnetic B and electric fields E and also switch the electric charge e with the magnetic charge g of a magnetic "monopole": E <--> B and e <--> g (In fact, the product eg is a constant.)

Here's another discussion of magnetic monopoles and duality, from an e-book on quantum gravity:

<a href="http://adela.karlin.mff.cuni.cz/~motl/Gibbs/strings.htm" target="_blank">http://adela.karlin.mff.cuni.cz/~motl/Gibbs/strings.htm</a>

Quote:

Dualities

In the past couple of years there have been some new developments which have inspired a revival of interest in string theory. The first of these concerns duality between electric and magnetic monopoles.

Maxwell's equations for electromagnetic waves in free space are symmetric between electric and magnetic fields. A changing magnetic field generates an electric field and a changing magnetic field generates an electric one. The equations are the same in each case, apart from a sign change which is irrelevant here. However, it is an experimental fact that there are no magnetic monopole charges in nature which mirror the electric charge of electrons and other particles. Despite some quite careful experiments only dipole magnetic fields which are generated by circulating electric charges have ever been observed.

In classical electrodynamics there is no inconsistency in a theory which places both magnetic and electric monopoles together. In quantum electrodynamics this is not so easy. To quantise Maxwell's equations it is necessary to introduce a vector potential field from which the electric and magnetic fields are derived by differentiation. This procedure can not be done in a way which is symmetric between the electric and magnetic fields.

40 years ago Paul Dirac was not convinced that this ruled out the existence of magnetic monopoles. He always professed that he was motivated by mathematical beauty in physics. He tried to formulate a theory in which the gauge potential could be singular along a string joining two magnetic charges in such a way that the singularity could be displaced through gauge transformations and must therefore be considered physically inconsequential. The theory was not quite complete but it did have one saving grace. It provided a tidy explanation for why electric charges must be quantised as multiples of a unit of electric charge.

In the 1970's it was realised by 't Hooft and Polyakov that grand unified theories which might unify the strong and electro-weak forces would get around the problem of the singular gauge potential because they had a more general gauge structure. In fact these theories would predict the existence of magnetic monopoles. Even their classical formulation could contain these particles which would form out of the matter fields as topological solitons.

There is a simple model which gives an intuitive idea of what a topological soliton is. Imagine first a straight wire pulled tight like a washing line with many clothes pegs strung along it. Imagine that the clothes pegs are free to rotate about the axis of the line but that each one is attached to its neighbours by elastic bands on the free ends. If you turn up one peg it will pull those nearby up with it. When it is let go it will swing back like a pendulum but the energy will be carried away by waves which travel down the line. The angle of the pegs approximate a field along the one dimensional line. The equation for the dynamics of this field is known as the sine-Gordon equation. It is a pun on the Klien-Gordon equation which is the correct linear equation for a scalar field and which is the first order approximation to the sine-Gordon equation for small amplitude waves. If the sine-Gordon equation is quantised it will be found to be a description of interacting scalar fields in one dimension.

The interesting behaviour of this system appears when some of the pegs are swung through a large angle of 360 degrees over the top of the line. If you grab one peg and swing it over in this way you would create two twists in the opposite sense around the line. These twists are quite stable and can be made to travel up and down the line. A twist can only be made to disappear in a collision with a twist in the opposite direction.

These twists are examples of topological solitons. They can be regarded as being like particles and antiparticles but they exist in the classical physics system and are apparently quite different from the scalar particles of the quantum theory. In fact the solitons also exist in the quantum theory but they can only be understood non-perturbatively. So the quantised sine-Gordon equation has two types of particle which are quite different.

What makes this equation so remarkable is that there is a non-local transformation of the field which turns it into another one dimensional equation known as the Thirring model. The transformation maps the soliton particles of the sine-Gordon equation onto the ordinary quantum excitations of the Thirring model, so the two types of particle are not so different after all. We say that there is a duality between the two models, the sine-Gordon and the Thirring. They have different equations but they are really the same.

The relevance of this is that the magnetic monopoles predicted in GUT's are also topological solitons, though the configuration in three dimensional space is more difficult to visualise than for the one dimensional of the clothes line. Wouldn't it be nice if there was a similar duality between electric and magnetic charges as the one discovered for the sine-Gordon equation? If there was then a duality between electric and magnetic fields would be demonstrated. It would not quite be a perfect symmetry because we know that magnetic monopoles must be very heavy if they exist.

In 1977 Olive and Montenen conjectured that this kind of duality could exists, but the mathematics of field theories in 3 space dimensions is much more difficult than that of one dimension and it seems beyond hope that such a duality transformation can be constructed. But they made one step further forward. They showed that the duality could only exist in a supersymmetric version of a GUT. This is quite tantalising given the increasing interest in supersymmetric GUT's which are now considered more promising than the ordinary variety of GUT's for a whole host of reasons.

Until 1994 most physicists thought that there was no good reason to believe that there was anything to the Olive-Montenen conjecture. Then Seiberg and Witten made a fantastic breakthrough. By means of a special set of equations they demonstrated that a certain supersymmetric field theory did indeed exhibit electro-magnetic duality. As a bonus their method can be used to solve many unsolved problems in topology and physics.

Now at last we turn to string theory with the realisation that duality in string theory is very natural. In the last year physicists have discovered how to apply tests of duality to different string and p-brane theories in various dimensions. A series of conjectures have been made and tested. This does not prove that the duality is correct but each time a test has had the potential to show an inconsistency it has failed to destroy the conjectures. What makes this discovery so useful is that the dualities are a non-perturbative feature of string theory. Now many physicists see that p-brane theories can be as interesting as string theories in a non-perturbative setting. The latest result in this effort is the discovery that all four string theories which are known to be perturbatively finite are now thought to be derivable from a single theory in 11 dimensions known as M-theory. M-theory is a hypothetical quantum field theory which describes 2-branes and 5-branes related through a duality.

It would be wrong to say that very much of this is understood yet. There is still nothing like a correct formulation of M-theory or p-brane theories in their full quantum form, but there is new hope because now it is seen that all the different theories can be seen as part of one unique theory.

Steven S · 09-29-2002, 07:53 AM

Quote:

Originally posted by Feather:
[QB]

Charge isn't necessarily related to planck's constant in any fundamental way.

Huh? The electric charge is related to plank's constant and c through the fine structure constant. That's a pretty deep fundamental relation.

Steven S

Feather · 09-29-2002, 10:15 AM

Quote:

Originally posted by Steven S:


Huh? The electric charge is related to plank's constant and c through the fine structure constant. That's a pretty deep fundamental relation.

Steven S

Yes, I know this. When you show how the concept of charge derives from the fine structure constant please let me know (after you've picked up your Nobel Prize check)*. The fine structure constant can be derived from the other quantities based on the configuration of things which have charge by definition. It comes from the quantization of orbits in an atom composed of charged bits.

Maybe I'm just being overly pedantic when interpreting the "order" in which the relation goes.

*Note: it is my understanding that the fine structure constant has never been derived from first principles--that is, one must require the concept of charge a priori to obtain it. But, as I stated before, I haven't completed my training (in fact, I just started my advanced training), so I'm willing to accept that I may be ignorant of the facts here. No slight, offense, or pig-headedness on my part (intended) here.

[ September 29, 2002: Message edited by: Feather ]

09-29-2002, 03:51 AM	#5
Jesse Moderator - Science Discussions Join Date: Feb 2001 Location: Providence, RI, USA Posts: 9,908	Answerer: Thanks again, anyway, if magnetic monopoles are found to be in actual existence, don't this destory the stand that magnetism is merely a relativistic effect of the eletric force? It wouldn't change the fact that for matter that does not contain magnetic monopoles, the magnetic field can be derived as a consequence of the coulomb force and relativity. Even the theories that postulate magnetic monopoles do not say that they are the cause of magnetism in normal matter--they are expected to be pretty rare, I believe. The existence of magnetic monopoles might just demonstrate that the relation between coulomb and magnetic forces is completely symmetrical, since uncharged magnetic monopoles would presumably generate a coulomb force when you move them around, as a consequence of relativity again. [ September 29, 2002: Message edited by: Jesse ]</p>

09-29-2002, 05:59 AM	#6
Answerer Veteran Member Join Date: Feb 2002 Location: Singapore Posts: 3,956	Well, are you suggesting that if magnetic monopoles are to be discovered, they can't be static or stationary and are sure to move about and generating electric force at the same time? Anyway, how are magnetic charges(if there is) and electric charges related to planck constant? [ September 29, 2002: Message edited by: Answerer ]</p>

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09-28-2002, 07:50 PM	#1
Answerer Veteran Member Join Date: Feb 2002 Location: Singapore Posts: 3,956	Is magnetism a relativistic phenomenon? Hi guys, I realize that no one here like to discuss magnetism, nevertheless, I have some questions that need some answers. Please help me out: 1)Is magnetism a relativistic phenomenon of electric force and if so, why? 2)Or is magnetism a force created by magnetic monopole(if there is such a thing)?

09-28-2002, 08:24 PM	#2
Jesse Moderator - Science Discussions Join Date: Feb 2001 Location: Providence, RI, USA Posts: 9,908	#1. Since magnetism only appears when you have moving charges, it has to do with Lorentz contraction due to charges moving relative to one another--here's a page summarizing how it works: <a href="http://physics.weber.edu/schroeder/mrr/MRRtalk.html" target="_blank">http://physics.weber.edu/schroeder/mrr/MRRtalk.html</a>

09-29-2002, 02:56 AM	#3
Answerer Veteran Member Join Date: Feb 2002 Location: Singapore Posts: 3,956	Thanks again, anyway, if magnetic monopoles are found to be in actual existence, don't this destory the stand that magnetism is merely a relativistic effect of the eletric force?

09-29-2002, 03:26 AM	#4
Feather Veteran Member Join Date: May 2002 Location: Gainesville, FL Posts: 1,827	Now that's an interesting take on things. Hell, I've never been exposed to this treatment. Of course, I just started grad school last month. Of course, if a magnetic monopole were discovered, that'd toss this particular treatment right out the window as a mere mathematical oddity. Or it could have implications for quantum mechanics (why should the existence of a given class of particle interact just so?). Fortunately electromagnetic theory as it is usually taught now would not change overmuch, since the introduction of a magnetic monopole preserves the symmetry in Maxwell's Equations.

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